IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v67y2021i8p4935-4960.html
   My bibliography  Save this article

Size Matters, So Does Duration: The Interplay Between Offer Size and Offer Deadline

Author

Listed:
  • Zhenyu Hu

    (Institute of Operations Research and Analytics, National University of Singapore, Singapore 119260; Department of Analytics and Operations, Business School, National University of Singapore, Singapore 119245)

  • Wenjie Tang

    (Institute of Operations Research and Analytics, National University of Singapore, Singapore 119260; Faculty of Business, Economics, and Statistics, University of Vienna, 1090 Vienna, Austria)

Abstract

This paper investigates the interplay between offer size and offer deadline in a Stackelberg game involving a proposer and a responder. The proposer acts first by making an offer to the responder with a deadline, and the responder, concurrently following a continuous-time finite-horizon search for alternative offers, has to respond to the proposer’s offer by the deadline. Taking into account the responder’s reaction, the proposer’s optimal strategy can vary from an exploding offer—an offer that has to be accepted or rejected on the spot—to an offer with an extended deadline under different market conditions, proxied by characteristics of the alternative offer distribution. In particular, the proposer should offer an exploding offer when the alternative offer market is unfavorable to the responder, and the harsher it is, the smaller will be the offer size. By contrast, when the alternative offer market is favorable to the responder, the proposer can benefit from making a smaller (compared with the exploding offer) nonexploding offer, and the more favorable the market, the smaller will be the offer size and the longer the deadline. Our analysis is further extended to the case where the responder has private knowledge of the alternative offers’ arrival rate, and we characterize the optimal strategy for the proposer when she makes either a single offer or a menu of offers that serves as a self-selection mechanism. In the latter case, the optimal menu of offers can be implemented as a sign-up bonus type of contract.

Suggested Citation

  • Zhenyu Hu & Wenjie Tang, 2021. "Size Matters, So Does Duration: The Interplay Between Offer Size and Offer Deadline," Management Science, INFORMS, vol. 67(8), pages 4935-4960, August.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4935-4960
    DOI: 10.1287/mnsc.2020.3731
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2020.3731
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2020.3731?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Gantner, Anita, 2008. "Bargaining, search, and outside options," Games and Economic Behavior, Elsevier, vol. 62(2), pages 417-435, March.
    3. Arnold, Michael A. & Lippman, Steven A., 2000. "Elasticity of demand for search," Economics Letters, Elsevier, vol. 67(3), pages 309-314, June.
    4. Shirish D. Chikte & Sudhakar D. Deshmukh, 1987. "The Role of External Search in Bilateral Bargaining," Operations Research, INFORMS, vol. 35(2), pages 198-205, April.
    5. George J. Stigler, 1962. "Information in the Labor Market," NBER Chapters, in: Investment in Human Beings, pages 94-105, National Bureau of Economic Research, Inc.
    6. Gerard J. van den Berg, 1990. "Nonstationarity in Job Search Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 255-277.
    7. Steven Lippman & John McCall, 1993. "Search and the development of the economics of information," Estudios de Economia, University of Chile, Department of Economics, vol. 20(2 Year 19), pages 223-249, December.
    8. Abhinay Muthoo, 1995. "On the Strategic Role of Outside Options in Bilateral Bargaining," Operations Research, INFORMS, vol. 43(2), pages 292-297, April.
    9. Saša Zorc & Ilia Tsetlin, 2020. "Deadlines, Offer Timing, and the Search for Alternatives," Operations Research, INFORMS, vol. 68(3), pages 927-948, May.
    10. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey: Part I," Economic Inquiry, Western Economic Association International, vol. 14(2), pages 155-189, June.
    11. Muriel Niederle & Alvin E. Roth, 2009. "Market Culture: How Rules Governing Exploding Offers Affect Market Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 199-219, August.
    12. Burdett, Kenneth & Mortensen, Dale T, 1998. "Wage Differentials, Employer Size, and Unemployment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 257-273, May.
    13. Wolinsky, Asher, 1987. "Matching, search, and bargaining," Journal of Economic Theory, Elsevier, vol. 42(2), pages 311-333, August.
    14. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    15. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    16. Chatterjee, Kalyan & Lee, Ching Chyi, 1998. "Bargaining and Search with Incomplete Information about Outside Options," Games and Economic Behavior, Elsevier, vol. 22(2), pages 203-237, February.
    17. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey," Economic Inquiry, Western Economic Association International, vol. 14(3), pages 347-368, September.
    18. Nelson Lau & Yakov Bart & J. Neil Bearden & Ilia Tsetlin, 2014. "Exploding Offers Can Blow Up in More Than One Way," Decision Analysis, INFORMS, vol. 11(3), pages 171-188, September.
    19. H. Dharma Kwon & Steven A. Lippman, 2011. "Acquisition of Project-Specific Assets with Bayesian Updating," Operations Research, INFORMS, vol. 59(5), pages 1119-1130, October.
    20. H. Dharma Kwon, 2010. "Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream," Operations Research, INFORMS, vol. 58(3), pages 638-649, June.
    21. Glenn Ellison & Alexander Wolitzky, 2012. "A search cost model of obfuscation," RAND Journal of Economics, RAND Corporation, vol. 43(3), pages 417-441, September.
    22. Stahl, Dale O, II, 1989. "Oligopolistic Pricing with Sequential Consumer Search," American Economic Review, American Economic Association, vol. 79(4), pages 700-712, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Manel Baucells & Steven A. Lippman, 2004. "Bargaining with Search as an Outside Option: The Impact of the Buyer's Future Availability," Decision Analysis, INFORMS, vol. 1(4), pages 235-249, December.
    2. Saša Zorc & Ilia Tsetlin, 2020. "Deadlines, Offer Timing, and the Search for Alternatives," Operations Research, INFORMS, vol. 68(3), pages 927-948, May.
    3. Armstrong, Mark & Zhou, Jidong, 2010. "Exploding offers and buy-now discounts," MPRA Paper 22531, University Library of Munich, Germany.
    4. Nicolas Jacquemet & Olivier L’Haridon & Isabelle Vialle, 2014. "Marché du travail, évaluation et économie expérimentale," Revue française d'économie, Presses de Sciences-Po, vol. 0(1), pages 189-226.
    5. Gantner, Anita, 2008. "Bargaining, search, and outside options," Games and Economic Behavior, Elsevier, vol. 62(2), pages 417-435, March.
    6. Anita Gantner, 2007. "Bargaining, Search, and Outside Options," Working Papers 2007-16, Faculty of Economics and Statistics, Universität Innsbruck.
    7. Nicolas Jacquemet & Olivier L’Haridon & Isabelle Vialle, 2014. "Marché du travail, évaluation et économie expérimentale," Revue française d'économie, Presses de Sciences-Po, vol. 0(1), pages 189-226.
    8. Fiona Scott Morton & Jorge Silva-Risso & Florian Zettelmeyer, 2011. "What matters in a price negotiation: Evidence from the U.S. auto retailing industry," Quantitative Marketing and Economics (QME), Springer, vol. 9(4), pages 365-402, December.
    9. Bruce I. Carlin & Florian Ederer, 2019. "Search Fatigue," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 54(3), pages 485-508, May.
    10. Charness, Gary & Kuhn, Peter, 2011. "Lab Labor: What Can Labor Economists Learn from the Lab?," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 3, pages 229-330, Elsevier.
    11. Bruce Carlin & Arna Olafsson & Michaela Pagel, 2017. "FinTech Adoption Across Generations: Financial Fitness in the Information Age," NBER Working Papers 23798, National Bureau of Economic Research, Inc.
    12. Steven A. Lippman & John W. Mamer, 2012. "Exploding Offers," Decision Analysis, INFORMS, vol. 9(1), pages 6-21, March.
    13. Chatterjee, Kalyan & Das, Kaustav, 2017. "Bilateral trading and incomplete information: Price convergence in a small market," Games and Economic Behavior, Elsevier, vol. 106(C), pages 89-113.
    14. Siqi Pan & Xin Zhao, 2023. "Commitment and cheap talk in search deterrence," RAND Journal of Economics, RAND Corporation, vol. 54(2), pages 325-359, June.
    15. Rami Zwick & Ching Chyi Lee, 1999. "Bargaining and Search: An Experimental Study," Group Decision and Negotiation, Springer, vol. 8(6), pages 463-487, November.
    16. Adina D. Sterling, 2014. "Friendships and Search Behavior in Labor Markets," Management Science, INFORMS, vol. 60(9), pages 2341-2354, September.
    17. Chatterjee, Kalyan & Lee, Ching Chyi, 1998. "Bargaining and Search with Incomplete Information about Outside Options," Games and Economic Behavior, Elsevier, vol. 22(2), pages 203-237, February.
    18. Brigitte Dormont & Denis Fougère & Ana Prieto, 2001. "L'effet de l'allocation unique dégressive sur la reprise d'emploi," Économie et Statistique, Programme National Persée, vol. 343(1), pages 3-28.
    19. Chantal Cases, 1996. "Assurance-chômage et offre de travail," Économie et Statistique, Programme National Persée, vol. 291(1), pages 139-150.
    20. Churlzu Lim & J. Neil Bearden & J. Cole Smith, 2006. "Sequential Search with Multiattribute Options," Decision Analysis, INFORMS, vol. 3(1), pages 3-15, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4935-4960. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.